Variance of Poisson λ = 5 = ?

A defining property of the Poisson distribution is that its variance equals its mean, and both are equal to λ. Since the question states λ = 5, the variance is also 5. This property distinguishes the Poisson distribution from many other probability distributions. The mean represents the expected number of events per interval, while the variance describes the spread of the event count around that mean. In a Poisson model with λ = 5, event counts tend to vary around 5, and the numerical variance is 5. Option B, 4, option C, 0, and option D, 1, do not follow from the Poisson variance rule. The result is not obtained by squaring λ or taking its square root; it is simply equal to λ. Study Guide references/topics: Poisson distribution, variance, mean, λ parameter.

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